DOI QR코드

DOI QR Code

A NOTE ON THE HYPER-ORDER OF ENTIRE FUNCTIONS

  • Lu, Feng (College of Science China University of Petroleum) ;
  • Qi, Jianming (Department of Mathematics and Physics Shanghai dianji university)
  • Received : 2012.08.08
  • Published : 2013.07.31

Abstract

In the paper, we have two purposes. Firstly, we estimate the hyper-order of an entire function which shares two functions with it's first derivative, and two examples are given to show the conclusion is sharp. Secondly, we generalize the Br$\ddot{u}$ck conjecture with the idea of sharing functions.

Keywords

References

  1. S. Bank and I. Laine, On the oscillation theory of f" + A(z)f = 0 where A is entire, Trans. Amer. Math. Soc. 273 (1982), no. 1, 351-363.
  2. P. D. Barry, On a theorem of Besicovitch, Quart. J. Math. Oxford Ser. (2) 14 (1963), 293-320. https://doi.org/10.1093/qmath/14.1.293
  3. R. Bruck, On entire functions which share one value CM with their first derivatives, Results Math. 30 (1996), no. 1-2, 21-24. https://doi.org/10.1007/BF03322176
  4. A. Chen, F. Lu, and H. X. Yi, Value sharing of meromorphic functions and their derivatives, J. Math. Anal. Appl. 359 (2009), no. 2, 696-703. https://doi.org/10.1016/j.jmaa.2009.06.024
  5. Z. X. Chen and Z. L. Zhang, Entire functions sharing fixed points with their higher order derivatives, Acta Math. Sinica (Chin. Ser.) 50 (2007), no. 6, 1213-1222.
  6. J. Grahl and C. Meng, Entire functions sharing a polynomial with their derivatives and normal families, Analysis (Munich) 28 (2008), no. 1, 51-61.
  7. I. Laine, Nevanlinna Theory and Complex Differential Equations, de Gruyter Studies in Mathematics, 15. Walter de Gruyter & Co., Berlin, 1993.
  8. X. M. Li and C. C. Gao, Entire functions sharing one polynomial with their derivatives, Proc. Indian Acad. Sci. Math. Sci. 118 (2008), no. 1, 13-26. https://doi.org/10.1007/s12044-008-0002-z
  9. X. J. Liu, S. Nevo, and X. C. Pang, On the kth derivative of meromorphic functions with zeros of multiplicity at least k+1, J. Math. Anal. Appl. 348 (2008), no. 1, 516-529. https://doi.org/10.1016/j.jmaa.2008.07.019
  10. F. Lu, J. F. Xu, and A. Chen, Entire functions sharing polynomials with their first derivatives, Arch. Math. (Basel) 92 (2009), no. 6, 593-601. https://doi.org/10.1007/s00013-009-3075-8
  11. F. Lu and H. X. Yi, On the uniqueness problems of meromorphic functions and their linear differential polynomials, J. Math. Anal. Appl. 362 (2010), no. 2, 301-312. https://doi.org/10.1016/j.jmaa.2009.09.027
  12. H. X. Yi and C. C. Yang, Uniqueness Theory of Meromorphic Functions, Science Press, Beijing, 1995.
  13. J. Zhang and L. W. Liao, On Bruck's conjecture on entire functions sharing one value with their derivatives, Houston. J. Math. 36 (2010), no. 2, 665-674.

Cited by

  1. Growth of Meromorphic Function Sharing Functions and Some Uniqueness Problems vol.2016, 2016, https://doi.org/10.1155/2016/6250867
  2. th Derivatives vol.2018, pp.2314-8888, 2018, https://doi.org/10.1155/2018/1298343